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Discovering time series motifs of all lengths using dynamic time warping

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Abstract

Motif discovery is a fundamental operation in the analysis of time series data. Existing motif discovery algorithms that support Dynamic Time Warping require manual determination of the exact length of motifs. However, setting appropriate length for interesting motifs can be challenging and selecting inappropriate motif lengths may result in valuable patterns being overlooked. This paper addresses the above problem by proposing algorithms that automatically compute motifs of all lengths using Dynamic Time Warping. Specifically, a batch algorithm as well as an anytime algorithm are designed in this paper, which are refered as BatchMotif and AnytimeMotif respectively. The proposed algorithms achieve significant improvements in efficiency by fully leveraging the correlations between the motifs of different lengths. Experiments conducted on real datasets demonstrate the superiority of both of the proposed algorithms. On average, BatchMotif is 13 times faster than the baseline method. Additionally, AnytimeMotif is 7 times faster than the baseline method and is capable of providing relatively satisfying results with only a small portion of calculation.

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Notes

  1. In this paper, the term "candidate" refers to a pair of subsequences of equal length. Because \(L_{\min }< L_{\max }<<n\), there are about \(O(n^2)\) pairs of candidates for a fixed motif length.

  2. Set \(\hat{S}_i^L[t] \leftarrow -\hat{S}_i^L[t]\), \(\hat{S}_i^{L+K}[t] \leftarrow -\hat{S}_i^{L+K}[t]\), \(u_t \leftarrow -v_t\), \(u_t \leftarrow -v_t\), \(u'_t \leftarrow -v'_t\), \(u'_t \leftarrow -v'_t\). Clearly, such a permutation does not affect the value of \(LB_{Keogh}\). Then you can find it is identical to the previous case.

  3. \(LB_{Keogh2}\),\(LB_{Keogh4}\),...,\(LB_{Keogh16}\) are the downsampling variants of \(LB_{Keogh}\), they are faster but less effective.

  4. In our paper, the top-1 ED motif is computed using STOMP [15] algorithm.

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Acknowledgements

Thanks to Dr. Zhixin Qi and Yonghang Yu for proofreading the paper.

Funding

This work is supported by National Natural Science Foundation of China (NSFC) Grant NOs. U19A2059, U22A2025, U1811461, 61972110, 61832003, 61872105, 62072136.

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Authors and Affiliations

  1. School of Computer Science and Technology, Harbin Institute of Technology, Harbin, 150001, Heilongjiang Province, China

    Zemin Chao, Hong Gao, Dongjing Miao & Hongzhi Wang

  2. School of Computer Science and Technology, Zhejiang Normal University, Jinhua, 321000, Zhejiang Province, China

    Hong Gao

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  1. Zemin Chao
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Contributions

Zemin Chao provides the main idea for the paper and conducts the experiments. Hong Gao and Dongjing Miao are responsible for designing the experiments and algorithms. Hongzhi Wang provides valuable suggestions to improve the algorithms and played a crucial role in writing the manuscript.

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Correspondence to Hong Gao.

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Chao, Z., Gao, H., Miao, D. et al. Discovering time series motifs of all lengths using dynamic time warping. World Wide Web 26, 3815–3836 (2023). https://doi.org/10.1007/s11280-023-01207-6

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  • DOI: https://doi.org/10.1007/s11280-023-01207-6

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